This research presents a systematic design procedure for supplemental viscoelastic dampers required to satisfy the given performance objectives using capacity spectrum method. To obtain required damper size, the amount of supplemental damping was computed from effective damping minus equivalent damping and inherent damping of structure. In the case of viscoelastic damper, iterative procedure is required because of the inherent stiffness of the damper. To verify the design method proposed in this study, parametric studies were performed for single degree of freedom systems with design variables. The method was also applied to a 10-story steel framed structure and the earthquake responses were obtained. According to time history analysis result the controlled displacements turned out to be close to the target displacement regardless of the design parameters.